Simultaneous Autoregressive Models Research Articles

High plant endemism in China is partially linked to reduced glacial‐interglacial climate change

AbstractAimEndemic species are hypothesized to particularly occur in areas with relatively stable climates during the Quaternary glacial‐interglacial oscillations (orbitally forced species' range dynamics hypothesis). This hypothesis has received support in global studies and studies from regions highly affected by glaciations. Here, we test its applicability to Chinese endemic species, thereby testing it in a region that was relatively mildly affected by glaciations.LocationChina.MethodsWe tested for associations between endemic species richness and Quaternary climate change, current climate and topography. Changes in mean annual temperature (MAT) and annual precipitation (MAP) between the Last Glacial Maximum and present were used to describe Quaternary climate change. We used simultaneous autoregressive (SAR) models to account for spatial autocorrelation in predictors, and Random Forest modelling to deal with non‐linear relationships and better handle multicollinearity among predictor variables. To get a deeper understanding of the mechanisms involved we also performed analyses based on growth‐form (woody versus herbaceous plants) and species age (palaeo‐ and neoendemics).ResultsSingle‐predictor SAR models showed that glacial‐interglacial MAT velocity always has higher explanatory power than current climate (with a pseudo r2 difference of 0.581–0.604 between the best palaeoclimate and current climate predictors for models for all endemic plants). Model selection on multivariate SAR models (based on Akaike weights) and Random Forest modelling (based on correlations between predicted and observed species richness) always included at least one variable representing Quaternary climate change as well as one or more current climate variables. Quaternary climate‐change variables were generally of similar strength to the current climate predictors. Notably, the summed Akaike weight across all models in the relevant model set was always 1 for glacial‐interglacial MAT velocity. There were no clear differences with respect to growth forms or species age in the estimated importance of Quaternary climate change.Main conclusionsThe consistent association between long‐term climatic stability and high plant endemism in China provides strong evidence for the importance of Quaternary glacial‐interglacial climate changes in shaping the distribution of endemic species, even in regions relatively mildly affected by glaciations. Hence, even moderate climate changes may have strong, long‐term effects on species diversity patterns.

Spatial autocorrelation in fitness affects the estimation of natural selection in the wild

Summary Natural selection is typically estimated in the wild using Lande and Arnold's multiple regression approach. Despite its utility for evolutionary ecologists, this method is subject to the classical assumptions of multiple regressions, which could result in potential analytical problems. In particular, spatial autocorrelation in fitness violates the assumption of residuals independence. Although widespread in the wild, the consequences of this effect have yet to be investigated in the context of Lande and Arnold's regression and resulting selection estimation. Here we first described four spatially explicit models that allow to control for spatial autocorrelation in residuals of the Lande and Arnold's regression: a generalized least square (GLS) model with a distance‐based exponential covariance function, two simultaneous autoregressive models (SAR, the lagged‐response model (SAR‐lag) and the spatial error model (SAR‐err)) and a 5‐step procedure using the principal coordinates of neighbour matrices (PCNM) method based on the extraction of spatial descriptors. We then compared the four spatially explicit models of selection to non‐spatial models for three life‐history traits recorded over 6 years in a wild blue tit (Cyanistes caeruleus) population. We also compared the performance of the four spatially explicit models of selection using a simulation approach. Our analyses revealed strong spatial autocorrelation in residuals of selection models, which was completely described by the two SAR and the PCNM models, while only partially described by the GLS model. The magnitude of selection gradients and differentials decreased systematically in the 4 spatially explicit models while the degree of fit of these models increased (except for the GLS model). Moreover, we showed using simulations that the selection coefficients extracted from the SAR‐lag model were systematically biased compared to those extracted from the GLS, SAR‐err and PCNM models. We hereby showed that spatial autocorrelation in fitness can severely affect selection differentials and gradients, even at a relatively small spatial scale. By using geostatistical models such as PCNM or SAR‐err models, it is possible to control for this spatial autocorrelation. Finally, since spatial autocorrelation is closely linked to spatial environmental variation, this approach can also be used to explore environmental components of covariance between fitness and traits.

Suitability of biodiversity-area and biodiversity-perimeter relationships in ecology: a case study of urban ecosystems

Urban areas are probably the most fragmented environments with respect to the presence of semi-natural habitats and shape of these habitats may be significantly affected by urbanization. Patch perimeter in landscape or habitat studies is much less popular to study than patch area. The studied sites were situated in the industrial city of Pardubice, which is one of the ten largest cities in the Czech Republic with nearly 100,000 inhabitants. In total, 40 grasslands were studied within a circular area of 314 km2. Butterflies and beetles with diurnal activity were studied during timed survey walks. A Simultaneous autoregressive model was used for test of the effect of biodiversity-area and biodiversity-perimeter relationships and for exclusion of potential bias caused by spatial autocorrelation. The models including patch perimeter performed better than those using patch area in explaining species richness, abundance and diversity of investigated organisms and were less influenced by spatial autocorrelation. The main conclusion and recommendation of the present study is that researchers should pay more attention to the possible influence of the patch perimeter as a potential predictor or co-predictor for landscape and habitat studies – especially in urban areas, where the negative effects of fragmentation might be much higher than in rural or more natural landscapes. Performing preliminary tests on comparisons between area and perimeter is highly recommended.

Bird diversity and environmental heterogeneity in North America: a test of the area–heterogeneity trade‐off

AbstractAimDeterministic niche theory predicts that increasing environmental heterogeneity increases species richness. In contrast, a recent stochastic model suggests that heterogeneity has a unimodal effect on species richness since high levels of heterogeneity reduce the effective area available per species, thereby increasing the likelihood of stochastic extinction (the ‘area–heterogeneity trade‐off’). We tested these contrasting predictions using data on bird distributions in North America.LocationNorth America.MethodsThe effect of heterogeneity on species richness was tested using simultaneous autoregressive regression models based on two measures of heterogeneity (elevational range and land‐cover richness) each quantified at two scales (400 m, 5 km), three measures of species richness (observed, corrected for incomplete detection, and corrected for regional richness) and three variable selection methods [forced entry, Akaike information criterion (AIC)‐based and a null‐model approach]. Covariates included precipitation, temperature, elevation and latitude. For all variables, both linear and quadratic terms were included in the analyses.ResultsOverall, heterogeneity had a weak effect on species richness and the contribution of the quadratic term of heterogeneity to the explained variance was very small (< 1%). Nevertheless, in all 36 models, the coefficients of both the linear and quadratic terms of heterogeneity were statistically significant and the estimated inflection point was within the range of the data, as predicted by the area–heterogeneity trade‐off. Moreover, in 30 out of the 36 models, support for a unimodal effect of heterogeneity on species richness based on information theoretic criteria was strong (ΔAIC > 10), and in 22 of those 30 models the null hypothesis of a monotonically positive relationship could be rejected at the 0.05% significance level.Main conclusionsPatterns of bird richness in North America were predominantly consistent with the predictions of the area–heterogeneity trade‐off. Future attempts to understand the mechanisms affecting species diversity should pay more attention to the potential consequences of this fundamental trade‐off.

Region-specific patterns and drivers of macroscale forest plant invasions

Aim Stronger inferences about biological invasions may be obtained when accounting for multiple invasion measures and the spatial heterogeneity occurring across large geographic areas. We pursued this enquiry by utilizing a multimeasure, multiregional framework to investigate forest plant invasions at a subcontinental scale. Location United States of America (USA). Methods Using empirical data from a national survey of USA forests, we compiled and mapped invasion richness (number of invasive species) and invasion prevalence (percentage of plots invaded) for 2524 counties. We then modelled each of these invasion measures as functions of 22 factors reflective of propagule pressure and/or habitat invasibility for eastern and western forests separately using simultaneous autoregressive spatial error models. Results Eastern forests had higher mean invasion richness (6.1) and prevalence (48%) than western forests (3.2 and 10%, respectively). Spatial patterns of invasion richness and prevalence differed, especially in the West. Propagule pressure factors were always positively associated with both invasion measures. Factors associated with human legacy were nearly six times more strongly associated with western than eastern invasions. Unlike propagule pressure factors, habitat invasibility factors shared inconsistent associations with invasion measures. Main conclusions The weaker associations between human legacy and invasions in the heavily invaded East, compared to the less-invaded West, suggest a declining effect of propagule pressure over time with increasing invasion intensity. The importance of propagule pressure in less-invaded western forests suggests that spatial variability in propagule inputs, coupled with lags between establishment and commonness, drives the spatial differences between invasion richness and prevalence during early invasion stages. Meanwhile, declining spatial disagreement between invasion measures and the relative unimportance of propagule pressure, in heavily invaded eastern forests, suggest that species-specific variation in response to habitat invasibility drives spatial differences between invasion measures during later invasion stages. These insights further illustrate the importance of spatial heterogeneity in invasive plant management and policy at macroscales.

Macroecological factors explain large-scale spatial population patterns of ancient agriculturalists

Aim: It has been well demonstrated that the large-scale distribution patterns of numerous species are driven by similar macroecological factors. However, understanding of this topic remains limited when applied to our own species. Here we take a large-scale look at ancient agriculturalist populations over the past two millennia. The main aim of this study was to test the hypothesis that the patterns of agriculturalist populations were shaped by relevant macroecological factors. Location: China. Methods: Using detailed historical census data, we reconstructed spatial patterns of human population density over 13 imperial dynasties in ancient China, which was dominated by agrarian societies. We used simultaneous autoregressive models to examine the population densities of agriculturalists in relation to climatic, topographic, edaphic and hydrological variables, together with the spatial structure of a concentration of population toward national capitals. The pure and shared effects of these variables and the population-concentration structure were decomposed using a variation partitioning procedure. Results: Spatial population patterns of ancient agriculturalists can be well modelled by climate, topography, soil properties and local hydrological systems. A plausible explanation is that by influencing crop yield these environmental factors essentially drive the distribution of agriculturalists. The population-concentration structure can also explain agriculturalist patterns to a considerable extent. This structure and those environmental factors have largely shared effects in simultaneously shaping these agriculturalist patterns. Main conclusions: While humans can effectively temper environmental constraints at small spatial scales, our results demonstrate that macroecological factors underpin the spatial patterns of humans at large scales. Macroecological constraints and their relative importance are found to be similar for humans and other species, suggesting that similar mechanisms are likely to underlie these macroecological patterns. Our findings have potential implications for the assessment of future responses of humans to global environmental changes.

베이지안 모형을 활용한 국내 노인 자살률 질병지도

Elderly suicide rates tend to be high in Korea. Suicide by the elderly is no longer a personal problem; consequently, further research on risk and regional factors is necessary. Disease mapping in epidemiology estimates spatial patterns for disease risk over a geographical region. In this study, we use a simultaneous conditional autoregressive model for spatial correlations between neighboring areas to estimate standard mortality ratios and mapping. The method is illustrated with cause of death data from 2006 and 2010 to analyze regional patterns of elderly suicide in Korea. By considering spatial correlations, the Bayesian spatial models, mean educational attainment and percentage of the elderly who live alone was the significant regional characteristic for elderly suicide. Gibbs sampling and grid method are used for computation.

Lean‐season primary productivity and heat dissipation as key drivers of geographic body‐size variation in a widespread marsupial

Geographic body‐size variation characterises many mammal species. Hypotheses centring around heat conservation, heat dissipation, primary productivity and seasonality have been advanced to explain geographic body‐size patterns. However, identification of the primary body‐size drivers has often been hampered by a paucity of data for broadly distributed species and the application of regression models that have not explicitly accounted for the spatial clustering inherent in such datasets. We used Australia's most widespread marsupial, the common brushtail possum Trichosurus vulpecula, as a model species with which to test five proposed drivers of geographic body‐size variation. Using geo‐referenced skull measurements from 588 specimens and a suite of putative environmental covariates, we employed spatial simultaneous autoregressive models, together with information criteria, to evaluate these different hypotheses. Our analysis identified a strong, positive relationship between possum body size and primary productivity during the least productive season, whereas the relationship with mean annual productivity received less support. Consistent with the heat‐dissipation hypothesis, T. vulpecula body size also decreased with increasing mean summer maximum temperature. Spatial autoregression coefficients estimated from the simultaneous autoregressive models were always high, suggesting that additional abiotic or biotic factors might contribute to the spatial patterns observed. We argue that the analysis of geographic body‐size variation should consider multi‐causal possibilities rather than treating the numerous hypotheses as competing, mutually exclusive alternatives.

Climate and species richness predict the phylogenetic structure of African mammal communities.

We have little knowledge of how climatic variation (and by proxy, habitat variation) influences the phylogenetic structure of tropical communities. Here, we quantified the phylogenetic structure of mammal communities in Africa to investigate how community structure varies with respect to climate and species richness variation across the continent. In addition, we investigated how phylogenetic patterns vary across carnivores, primates, and ungulates. We predicted that climate would differentially affect the structure of communities from different clades due to between-clade biological variation. We examined 203 communities using two metrics, the net relatedness (NRI) and nearest taxon (NTI) indices. We used simultaneous autoregressive models to predict community phylogenetic structure from climate variables and species richness. We found that most individual communities exhibited a phylogenetic structure consistent with a null model, but both climate and species richness significantly predicted variation in community phylogenetic metrics. Using NTI, species rich communities were composed of more distantly related taxa for all mammal communities, as well as for communities of carnivorans or ungulates. Temperature seasonality predicted the phylogenetic structure of mammal, carnivoran, and ungulate communities, and annual rainfall predicted primate community structure. Additional climate variables related to temperature and rainfall also predicted the phylogenetic structure of ungulate communities. We suggest that both past interspecific competition and habitat filtering have shaped variation in tropical mammal communities. The significant effect of climatic factors on community structure has important implications for the diversity of mammal communities given current models of future climate change.

How Do Climatic Predictors Affect Tree Richness in Western Ghats, India?

In this brief report, the relative importance of different climatic variables on structuring the spatial richness patterns of endemic tree species are quantified for Western Ghats of India, a biodiversity hotspot of the world. Path analysis and spatial multiple regression analysis are employed to measure the relative impacts of different climatic variables on the richness of tree species. Four climatic predictors, annual mean temperature (TEM), annual mean precipitation (PREC), annual evapotranspiration (AET), and elevation range (TOPO), are used to represent different perspectives of climatic variability. TEM represents temperature tolerance, PREC water availability, AET energy and TOPO habitat heterogeneity. Results show that, without removing spatial autocorrelation, AET is the most influential variable. However, the effect of AET was detected to be an artifact of spatial autocorrelation and after controlling such a misleading effect using simultaneous autoregressive models, the effects of other variables became evident and important in explaining the richness of endemic trees. All the statistical models consistently identified that TOPO and PREC are the equally influential variables for structuring richness patterns of endemic trees in Western Ghats. In conclusion, habitat heterogeneity and water availability are the most important predictors of richness in tropical endemic tree communities in Western Ghats.

Predicting functional connectivity from structural connectivity via computational models using MRI: An extensive comparison study

The relationship between structural connectivity (SC) and functional connectivity (FC) in the human brain can be studied using magnetic resonance imaging (MRI). However many of the underlying physiological mechanisms and parameters cannot be directly observed with MRI. This limitation has motivated the recent use of various computational models meant to bridge the gap. However their absolute and relative explanatory power and the properties that actually drive that power remain insufficiently characterized. We performed an extensive comparison of seven mainstream computational models predicting FC from SC. We investigated the extent to which simulated FC could predict empirical FC. We also applied graph theory to the entire set of simulated and empirical FCs in order to further characterize the relationships between the models and the MRI data. The comparison was performed at three different spatial scales. We found that (i) there were significant effects of scale and model on predictive power; (ii) among all models, the simplest model, the simultaneous autoregressive (SAR) model, was found to consistently perform better than the other models; (iii) the SAR also appeared more ‘central’ from a graph theory perspective; and (iv) empirical FC only appeared weakly correlated with simulated FCs, and was featured as ‘peripheral’ in the graph analysis. We conclude that the substantial differences existing between these computational models have little impact on their predictive power for FC and that their capacity to predict FC from SC appears to be both moderate and essentially underlined by a simple core linear process embodied by the SAR model.

Spatial Models for Prediction and Early Warning of Aedes aegypti Proliferation from Data on Climate Change and Variability in Cuba

Climate variability, the primary expression of climate change, is one of the most important environmental problems affecting human health, particularly vector-borne diseases. Despite research efforts worldwide, there are few studies addressing the use of information on climate variability for prevention and early warning of vector-borne infectious diseases. Show the utility of climate information for vector surveillance by developing spatial models using an entomological indicator and information on predicted climate variability in Cuba to provide early warning of danger of increased risk of dengue transmission. An ecological study was carried out using retrospective and prospective analyses of time series combined with spatial statistics. Several entomological and climatic indicators were considered using complex Bultó indices -1 and -2. Moran's I spatial autocorrelation coefficient specified for a matrix of neighbors with a radius of 20 km, was used to identify the spatial structure. Spatial structure simulation was based on simultaneous autoregressive and conditional autoregressive models; agreement between predicted and observed values for number of Aedes aegypti foci was determined by the concordance index Di and skill factor Bi. Spatial and temporal distributions of populations of Aedes aegypti were obtained. Models for describing, simulating and predicting spatial patterns of Aedes aegypti populations associated with climate variability patterns were put forward. The ranges of climate variability affecting Aedes aegypti populations were identified. Forecast maps were generated for the municipal level. Using the Bultó indices of climate variability, it is possible to construct spatial models for predicting increased Aedes aegypti populations in Cuba. At 20 x 20 km resolution, the models are able to provide warning of potential changes in vector populations in rainy and dry seasons and by month, thus demonstrating the usefulness of climate information for epidemiological surveillance.

Using Bootstrap Methods to Investigate Coefficient Non-stationarity in Regression Models: An Empirical Case Study

In this study, parametric bootstrap methods are used to test for spatial non-stationarity in the coefficients of regression models (i.e. test for relationship non-stationarity). Such a test can be rather simply conducted by comparing a model such as geographically weighted regression (GWR) as an alternative to a standard regression, the null hypothesis. However here, three spatially autocorrelated regressions are also used as null hypotheses: (i) a simultaneous autoregressive error model; (ii) a moving average error model; and (iii) a simultaneous autoregressive lag model. This expansion of null hypotheses, allows an investigation as to whether the spatial variation in the coefficients obtained using GWR could be attributed to some other spatial process, rather than one depicting non-stationary relationships. In this short presentation, the bootstrap approach is applied empirically to an educational attainment data set for Georgia, USA. Results suggest value in the bootstrap approach, providing a more informative test than any related test that is commonly applied.

Social stressors and air pollution across New York City communities: a spatial approach for assessing correlations among multiple exposures.

BackgroundRecent toxicological and epidemiological evidence suggests that chronic psychosocial stress may modify pollution effects on health. Thus, there is increasing interest in refined methods for assessing and incorporating non-chemical exposures, including social stressors, into environmental health research, towards identifying whether and how psychosocial stress interacts with chemical exposures to influence health and health disparities. We present a flexible, GIS-based approach for examining spatial patterns within and among a range of social stressors, and their spatial relationships with air pollution, across New York City, towards understanding their combined effects on health.MethodsWe identified a wide suite of administrative indicators of community-level social stressors (2008–2010), and applied simultaneous autoregressive models and factor analysis to characterize spatial correlations among social stressors, and between social stressors and air pollutants, using New York City Community Air Survey (NYCCAS) data (2008-2009). Finally, we provide an exploratory ecologic analysis evaluating possible modification of the relationship between nitrogen dioxide (NO2) and childhood asthma Emergency Department (ED) visit rates by social stressors, to demonstrate how the methods used to assess stressor exposure (and/or consequent psychosocial stress) may alter model results.ResultsAdministrative indicators of a range of social stressors (e.g., high crime rate, residential crowding rate) were not consistently correlated (rho = - 0.44 to 0.89), nor were they consistently correlated with indicators of socioeconomic position (rho = - 0.54 to 0.89). Factor analysis using 26 stressor indicators suggested geographically distinct patterns of social stressors, characterized by three factors: violent crime and physical disorder, crowding and poor access to resources, and noise disruption and property crimes. In an exploratory ecologic analysis, these factors were differentially associated with area-average NO2 and childhood asthma ED visits. For example, only the ‘violent crime and disorder’ factor was significantly associated with asthma ED visits, and only the ‘crowding and resource access’ factor modified the association between area-level NO2 and asthma ED visits.ConclusionsThis spatial approach enabled quantification of complex spatial patterning and confounding between chemical and non-chemical exposures, and can inform study design for epidemiological studies of separate and combined effects of multiple urban exposures.Electronic supplementary materialThe online version of this article (doi:10.1186/1476-069X-13-91) contains supplementary material, which is available to authorized users.

The unusual suspect: Land use is a key predictor of biodiversity patterns in the Iberian Peninsula

Although land use change is a key driver of biodiversity change, related variables such as habitat area and habitat heterogeneity are seldom considered in modeling approaches at larger extents. To address this knowledge gap we tested the contribution of land use related variables to models describing richness patterns of amphibians, reptiles and passerines in the Iberian Peninsula. We analyzed the relationship between species richness and habitat heterogeneity at two spatial resolutions (i.e., 10 km × 10 km and 50 km × 50 km). Using both ordinary least square and simultaneous autoregressive models, we assessed the relative importance of land use variables, climate variables and topographic variables. We also compare the species–area relationship with a multi-habitat model, the countryside species–area relationship, to assess the role of the area of different types of habitats on species diversity across scales. The association between habitat heterogeneity and species richness varied with the taxa and spatial resolution. A positive relationship was detected for all taxa at a grain size of 10 km × 10 km, but only passerines responded at a grain size of 50 km × 50 km. Species richness patterns were well described by abiotic predictors, but habitat predictors also explained a considerable portion of the variation. Moreover, species richness patterns were better described by a multi-habitat species-area model, incorporating land use variables, than by the classic power model, which only includes area as the single explanatory variable. Our results suggest that the role of land use in shaping species richness patterns goes beyond the local scale and persists at larger spatial scales. These findings call for the need of integrating land use variables in models designed to assess species richness response to large scale environmental changes.

Relating structural and functional connectivity in MRI: a simple model for a complex brain.

Advances in magnetic resonance imaging (MRI) allow to gain critical insight into the structure of neural networks and their functional dynamics. To relate structural connectivity [as quantified by diffusion-weighted imaging (DWI) tractography] and functional connectivity [as obtained from functional MRI (fMRI)], increasing emphasis has been put on computational models of brain activity. In the present study, we use structural equation modeling (SEM) with structural connectivity to predict functional connectivity. The resulting model takes the simple form of a spatial simultaneous autoregressive model (sSAR), whose parameters can be estimated in a Bayesian framework. On synthetic data, results showed very good accuracy and reliability of the inference process. On real data, we found that the sSAR performed significantly better than two other reference models as well as than structural connectivity alone, but that the Bayesian procedure did not bring significant improvement in fit compared to two simpler approaches. Nonetheless, we also found that the values of the region-specific parameters inferred using Bayesian inference differed significantly across resting-state networks. These results demonstrate 1) that a simple abstract model is able to perform better that more complex models based on more realistic assumptions, 2) that the parameters of the sSAR can be estimated and can potentially be used as biomarkers, but also 3) that the sSAR, while being the best-performing model, is at best still a very crude model of the relationship between structure and function in MRI.

The Influences of Species Richness and Climate on the Phylogenetic Structure of African Haplorhine and Strepsirrhine Primate Communities

Many factors contribute to the structure of primate communities, including historical processes, interspecific competition, and climate. Here, we quantify the phylogenetic structure of individual primate communities to evaluate these factors relative to a null model. Then, we examine the effects of species richness and local climate on variation in community phylogenetic structure. We analyze 71 haplorhine and 29 strepsirrhine communities in Africa and quantify their net relatedness (NRI) and nearest taxon (NTI) indices. Significantly low, i.e., phylogenetically even, NRI and NTI values are indicative of interspecific competition in the past, resulting in closely related species not being found in the same community. In contrast, significantly high, i.e., phylogenetically clustered, NRI and NTI values suggest that closely related species have similar ecological requirements, resulting in closely related species occupying the same community. In a second set of analyses, we used simultaneous autoregressive models to examine if species richness, rainfall, and temperature predict variation in community phylogenetic structure. Most individual communities exhibited phyloge- netically random species assemblages. However, significantly structured haplorhine

A quality assessment of eigenvector spatial filtering based parameter estimates for the normal probability model

Eigenvector spatial filtering, which introduces a subset of eigenvectors extracted from a spatial weights matrix as synthetic control variables in a regression model specification, furnishes a solution to extraordinarily intricate statistical modeling problems involving spatial dependences. It accounts for spatial autocorrelation in standard specifications of regression models. But the quality of the resulting regression parameter estimates has yet to be ascertained. The estimator properties to establish include unbiasedness, efficiency, and consistency. The purpose of this paper is to demonstrate these estimator properties for linear regression parameters based on eigenvector spatial filtering, including a comparison with the simultaneous autoregressive (SAR) model. Eigenvector spatial filtering methodology requires the judicious selection of eigenvectors, whose number tends to increase with both level of linear regression residual spatial autocorrelation and the number of areal units. A logistic regression description of the number of eigenvectors selected in a simulation pilot study suggests estimator consistency.

A spatially explicit approach to the study of socio-demographic inequality in the spatial distribution of trees across Boston neighborhoods.

The racial/ethnic and income composition of neighborhoods often influences local amenities, including the potential spatial distribution of trees, which are important for population health and community wellbeing, particularly in urban areas. This ecological study used spatial analytical methods to assess the relationship between neighborhood socio-demographic characteristics (i.e. minority racial/ethnic composition and poverty) and tree density at the census tact level in Boston, Massachusetts (US). We examined spatial autocorrelation with the Global Moran's I for all study variables and in the ordinary least squares (OLS) regression residuals as well as computed Spearman correlations non-adjusted and adjusted for spatial autocorrelation between socio-demographic characteristics and tree density. Next, we fit traditional regressions (i.e. OLS regression models) and spatial regressions (i.e. spatial simultaneous autoregressive models), as appropriate. We found significant positive spatial autocorrelation for all neighborhood socio-demographic characteristics (Global Moran's I range from 0.24 to 0.86, all P=0.001), for tree density (Global Moran's I=0.452, P=0.001), and in the OLS regression residuals (Global Moran's I range from 0.32 to 0.38, all P<0.001). Therefore, we fit the spatial simultaneous autoregressive models. There was a negative correlation between neighborhood percent non-Hispanic Black and tree density (rS=-0.19; conventional P-value=0.016; spatially adjusted P-value=0.299) as well as a negative correlation between predominantly non-Hispanic Black (over 60% Black) neighborhoods and tree density (rS=-0.18; conventional P-value=0.019; spatially adjusted P-value=0.180). While the conventional OLS regression model found a marginally significant inverse relationship between Black neighborhoods and tree density, we found no statistically significant relationship between neighborhood socio-demographic composition and tree density in the spatial regression models. Methodologically, our study suggests the need to take into account spatial autocorrelation as findings/conclusions can change when the spatial autocorrelation is ignored. Substantively, our findings suggest no need for policy intervention vis-à-vis trees in Boston, though we hasten to add that replication studies, and more nuanced data on tree quality, age and diversity are needed.

Landscape Heterogeneity–Biodiversity Relationship: Effect of Range Size

The importance of landscape heterogeneity to biodiversity may depend on the size of the geographic range of species, which in turn can reflect species traits (such as habitat generalization) and the effects of historical and contemporary land covers. We used nationwide bird survey data from Japan, where heterogeneous landscapes predominate, to test the hypothesis that wide-ranging species are positively associated with landscape heterogeneity in terms of species richness and abundance, whereas narrow-ranging species are positively associated with landscape homogeneity in the form of either open or forest habitats. We used simultaneous autoregressive models to explore the effects of climate, evapotranspiration, and landscape heterogeneity on the richness and abundance of breeding land-bird species. The richness of wide-ranging species and the total species richness were highest in heterogeneous landscapes, where many wide-ranging species showed the highest abundance. In contrast, the richness of narrow-ranging species was not highest in heterogeneous landscapes; most of those species were abundant in either open or forest landscapes. Moreover, in open landscapes, narrow-ranging species increased their species richness with decreasing temperature. These results indicate that heterogeneous landscapes are associated with rich bird diversity but that most narrow-ranging species prefer homogeneous landscapes—particularly open habitats in colder regions, where grasslands have historically predominated. There is a need to reassess the generality of the heterogeneity-biodiversity relationship, with attention to the characteristics of species assemblages determined by environments at large spatiotemporal scales.